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C2×ΓL(1,𝔽8)×D209 #31798286

order17556
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC2×ΓL(1,𝔽8)×D209
unambiguous semidirect product(C2×C11)⋊(ΓL(1,𝔽8)×D19)

Splittings

Fitting, socleC2×C7×C11×C19 ⋊ C2×C3
derived, HallC7×C11×C19 ⋊ C22×C3
HallC2×C7×D209 ⋊ C3
HallC11×C19×ΓL(1,𝔽8) ⋊ C22
HallC19×ΓL(1,𝔽8) ⋊ C2×D11
HallC11×ΓL(1,𝔽8) ⋊ C2×D19
HallC11×C19 ⋊ C22×ΓL(1,𝔽8)
HallC7×C19 ⋊ C2×C3×D11
HallC7×C11 ⋊ C2×C3×D19
SylowC19 ⋊ C2×ΓL(1,𝔽8)×D11
SylowC11 ⋊ C2×ΓL(1,𝔽8)×D19
SylowC7 ⋊ C2×C3×D209

Subgroups

subgroupG/H
center, hypercenterC2ΓL(1,𝔽8)×D209
commutator, cosocle, hypocenterC7×C11×C19C22×C3
FrattiniC1G
Fitting, socleC2×C7×C11×C19C2×C3
LCSG ▷ C7×C11×C19
UCSC1 ◁ C2

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2926

Conjugacy classes & character table

1060 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17556, 101);